Minkowski functionals are summary statistics that capture the geometric and morphological properties of fields. They are sensitive to all higher order correlations of the fields and can be used to complement more conventional statistics, such as the power spectrum of the field. We develop a Minkowski functional-based approach for a full likelihood analysis of mildly non-Gaussian sky maps with partial sky coverage. Applying this to the inference of cosmological parameters from the Planck mission's map of the Cosmic Microwave Background's lensing convergence, we find an excellent agreement with results from the power spectrum-based lensing likelihood. While the non-Gaussianity of current CMB lensing maps is dominated by reconstruction noise, a Minkowski functional-based analysis may be able to extract cosmological information from the non-Gaussianity of future lensing maps and thus go beyond what is accessible with a power spectrum-based analysis. We make the numerical code for the calculation of a map's Minkowski functionals, skewness and kurtosis parameters available for download from https://github.com/Kang-Yuqi/MF_lensing.

中文翻译：

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宇宙微波背景弱透镜收敛的闵可夫斯基泛函分析


闵可夫斯基泛函是捕获场的几何和形态特性的汇总统计量。它们对场的所有高阶相关性都很敏感，并且可用于补充更传统的统计数据，例如场的功率谱。我们开发了一种基于 Minkowski 函数的方法，用于对具有部分天空覆盖的轻度非高斯天空图进行完全似然分析。将其应用于从普朗克任务的宇宙微波背景透镜收敛图推断宇宙学参数时，我们发现与基于功率谱的透镜似然的结果非常一致。虽然当前 CMB 透镜图的非高斯性主要由重建噪声主导，但基于 Minkowski 函数的分析可能能够从未来透镜图的非高斯性中提取宇宙学信息，从而超越功率谱所能获得的信息。为基础的分析。我们提供了计算地图 Minkowski 泛函、偏度和峰度参数的数字代码，可从 https://github.com/Kang-Yuqi/MF_lensing 下载。